Question

Point of inflection given a graph

Answer 1

The graph is f ' (x), can someone explain to me why f(x) does have a point of inflection at x=3

Answer 2

The point of inflection of the function, f(x), is where a change in concavity occurs.
At this point, this is where the second derivative, f''(x) is equal to 0.

Answer 3

As you can see, at f'(3), the slope of the line tangent to that point will have a slope of 0.
Therefore, if we were to graph the second derivative, f''(3) = 0

Answer 4

ok thanks, now that makes sense.

Answer 5

In other words, extrema for the derivative of a function give you the inflection points for the function.

Answer 6

thanks everyone :)